Answer :
Final Answer:
In summary, the next time the two lighthouses will flash together is 1 minute and 45 seconds after 7 p.m.
Explanation:
To determine when the two lighthouses will flash together next, we need to find the least common multiple (LCM) of 21 seconds and 35 seconds.
One way to find the LCM is by listing the multiples of both numbers and identifying the smallest number that appears in both lists.
Multiples of 21: 21, 42, 63, 84, 105, ...
Multiples of 35: 35, 70, 105, 140, 175, ...
From the lists, we can see that the smallest number that appears in both lists is 105. Therefore, the two lighthouses will flash together again in 105 seconds.
To express the time in minutes and hours, we can divide 105 seconds by 60. The quotient is 1, indicating 1 minute, and the remainder is 45 seconds. Therefore, the two lighthouses will flash together again 1 minute and 45 seconds after they initially flash together at 7 p.m.
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